where \(\mathbf {z}\)  denotes the unknown discrete Fourier coefficients of each time frame and \(\mathcal {F}\)  denotes the Fourier transform operator. \(\Gamma \)  is defined as the feasible space of solutions (clipping consistency constraint, see Sec. REF ) [1]}:
\(\begin{split}\Gamma _R &= \lbrace  \tilde{\mathbf {x}} | M_R \tilde{\mathbf {x}} = M_R \mathbf {y} \rbrace , \\\Gamma _H &= \lbrace  \tilde{\mathbf {x}} | M_H \tilde{\mathbf {x}} \ge \theta _c \rbrace ,\end{split}\quad \begin{split}\Gamma _L &= \lbrace  \tilde{\mathbf {x}} | M_L \tilde{\mathbf {x}} \le - \theta _c \rbrace , \\\Gamma &= \Gamma _R \cap \Gamma _H \cap \Gamma _L,\end{split}\) 
